Bernstein polynomials for solving fractional heat- and wave-like equations

In this paper, a novel numerical analysis is introduced and performed to obtain the numerical solution of the fractional heat- and wave-like equations. A general formulation for the Bernstein fractional derivatives operational matrix is given. In this approach, a truncated Bernstein series together with the Bernstein operational matrix of fractional derivatives are used to reduce the solution of fractional differential problems to the solution of a system of algebraic equations. Numerical examples are considered aiming to demonstrate the validity and applicability of the proposed techniques and to compare with the existing results.